On a Time-Varying Parameter Adaptive Self-Organizing System in the Presence of Large Outliers in Observations

Abstract

In the previous papers (Pupeikis, 2000; Genov et al., 2006; Atanasov and Pupeikis, 2009), a direct approach for estimating the parameters of a discrete-time linear time-invariant (LTI) dynamic system, acting in a closed-loop in the case of additive noise with contaminating outliers uniformly spread in it, is presented. It is assumed there that the parameters of the LQG (Linear Quadratic Gaussian) controller are unknown, as well as known beforehand, too. The aim of the given paper is development of a minimum variance control (MVC) approach for a closed-loop discrete-time linear dynamic system when slowly or suddenly time-varying coefficients of the transfer function of such a system as well as that of a minimum variance (MV) controller are not known and ought to be estimated. The recursive parametric identification of an open-loop system and determination of the coefficients of the MV controller are performed in each current operation by processing observations in the case of additive noise at the output with contaminating outliers uniformly spread in it. The robust recursive technique, based on the S-algorithm, with a version of Shweppe's GM-estimator and with discounting previous data, used in the estimation, by introducing a constant as well as time-varying forgetting factors in the abovementioned estimator, is applied here in the calculation of estimates of the parameters of a dynamic system. Then, the recursive parameter estimates are used in each current iteration to determine unknown parameters of the MV controller. Afterwards, the current value of the MV control signal is found in each operation, and it is used to generate the output of the system, too. The results of numerical simulation by computer are presented and discussed.